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Consider the following snapshot of a system running n concurrent processes. Process i is holding X_i instances of a resource R, 1 ≤ i ≤ n. Assume that all instances of R are currently in use. Further, for all i, process i can place a request for up to Y_i additional instances of R while holding the X_i instances it already has. Of the n processes, there are exactly two processes p and q such that Yₚ = Y_q = 0. Which one of the following conditions guarantees that no other process apart from p and q can complete execution?

1. Xₚ + X_q < Min {Yₖ | 1 ≤ k ≤ n, k ≠ p, k ≠ q}
2. Xₚ + X_q < Max {Yₖ | 1 ≤ k ≤ n, k ≠ p, k ≠ q}
3. Min (Xₚ, X_q) ≤ Min {Yₖ | 1 ≤ k ≤ n, k ≠ p, k ≠ q}
4. Min (Xₚ, X_q) ≤ Max {Yₖ | 1 ≤ k ≤ n, k ≠ p, k ≠ q}

Correct answer: Xₚ + X_q < Min {Yₖ | 1 ≤ k ≤ n, k ≠ p, k ≠ q}

Solution

This condition ensures that the total resources held by processes p and q are less than the minimum resources that any other process can request, effectively preventing those processes from obtaining the resources they need to proceed, thus blocking their execution.

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